How to remap my UV without messing with textures already applied to a mesh?
You can have multiple UV maps on an object*.
With multiple UV maps you can keep your "old" UV map for the texturing you already did. Then add a second UV map and properly unwrap your object.

In the Object Data tab of the Properties window under the UV Maps heading, you will see something much like this:


Click on the + button, that will add another UV map slot to your object.

You really should name both your UVmaps now, just double click or CtrlLMB  on the name in the list to rename it.

Note: Be careful which UVmap is selected (highlighted in blue in the list), simply clicking on a UVmap will change what UVmap is selected or active. When you are unwrapping your object you will be changing the active UVmap.



Last step, go to everywhere you used the "old" UVmap: cycles nodes, BI material textures, modifiers, and dynamic paint, and make sure it is using the correct UVmap.

Now you can safely, in the new UVmap, unwrap your object however you like and it will not affect your previous texturing at all.



* In reality it is not added to the object, but the object data. However for brevity I will refer to it simply as the object.